Statistics And Probability Question 488
Question: The value of C for which $ P,(X=k)=Ck^{2} $ can serve as the probability function of a random variable X that takes 0, 1, 2, 3, 4 is
[EAMCET 1994]
Options:
A) $ \frac{1}{30} $
B) $ \frac{1}{10} $
C) $ \frac{1}{3} $
D) $ \frac{1}{15} $
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Answer:
Correct Answer: A
Solution:
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$ \sum\limits_{k=0}^{4}{P(X=k)}=1\Rightarrow \sum\limits_{k=0}^{4}{Ck^{2}}=1 $
$ \Rightarrow C(1^{2}+2^{2}+3^{2}+4^{2})=1\Rightarrow C=\frac{1}{30} $ .
BETA
